User blog:Mr. Bambu/Discworld Calc: The Piecemaker
Premise The Piecemaker is a big ballistae used as a personal crossbow for Detritus the Troll. From various statements, the weapon is said to be able to shoot through the entirety of a house (specifically Vimes Manor) and destroy any walls in between. Let's see if we can calc it. For backup, here's the statement. "As Detritus considers this a waste of energy if all the energy devoted to drawing back and cocking the string is only expended on a single arrow (which from a human point of view is a six-foot lance), he has adapted it still further, so that it shoots a bundle of twenty or so arrows wired together around a central core. Due to the violent force acting on them, the arrows tend to disintegrate into a cloud of supersonic (a significant fraction of local lightspeed) shrapnel which bursts into flame from air friction. The resulting fireball scythes everything in its path totally clean. Hence the name. It not only opens front doors, but frequently creates a back door as well." We will calculate the destruction values for "making a back door" first, then the KE of twenty supersonic 6-foot lances. Calc Making a Back Door First off, we will assume wooden walls (as are the norm for the time of the setting). We'll use this mansion floorplan as our basis. Assuming the shot goes through the maximum amount of walls, that's a grand total of 11 walls from the left side to the right. Comparing the length of the area (160 feet) to the front door, we get 4.58 feet for the width of the door. We'll therefore assume a width of 4.58 feet (139.60 cm). 1.45 (44.20 cm) feet is the width of the walls. Finally, we will assume a height of 4 meters (400 cm, duh) since this is a mansion and it is a reasonable assumption that the average room will have higher ceilings. We have our dimensions, making the standard wall's volume 2468128 cm^3. Multiply this by eleven for our eleven walls, we get 2.715 x 10^7 cm^3. We will assume V. Frag for our Low-End, Pulverization for our High-End. As we do not have any values for pulverizing or violently fragmenting wood (though we do have Fragmentation thanks to the article referenced here), we will find average values by taking the percentage of fragmentation value compared to v. frag and pulverization, and multiply wood's fragmentation value by that percentage. Percent Increase Concrete: V. Frag: 333% Pulverization: 667% Percent Increase Steel: V. Frag: 273% Pulverization: 481 % Percent Increase Iron: V. Frag: 212% Pulverization: 450% Percent Increase Glass: V. Frag: 133% Pulverization: 133333% (Disregarded due to outlier-ness). Percent Increase Ice: V. Frag: 157% Pulverization: 833% Percent Increase Human Body: V. Frag: 171% Pulverization: 293% Averages: V. Frag: 213% Pulverization: 545% So, we will apply these to our fragmentation value for wood (0.148 j/cc). New value for V. Frag on wood is 0.315 j/cc, and pulverization is 0.807 j/cc. Unsure of the validity of this, but this is the best method I know. Low-End: 2.715 x 10^7 cc x 0.315 j/cc = 8.552 x 10^6 Joules, or Wall level+ High-End: 2.715 x 10^7 cc = 2.191 x 10^7 Joules, or Room level. Anyways. Let's try KE. Supersonic Lances So, the statement says that it creates supersonic speeds and that the arrows are comparable to a six-foot lance, and that there are twenty. For the weight, we will assume a six foot long spear (182.88 cm) with a radius of 1.5 inches (3.81 cm). Volume of 8340 cubic centimeters, or 0.00834 cubic meters. Balsa Wood has a density of 160 kg per cubic meter. 1.334 kg is the weight of the shaft. According to this, the weight of the spear head is about .5 kg. So... 1.834 kg total. Total weight of all twenty spears is 36.68 kg. Now, for Supersonic Speed. For a Low-End, we will assume Mach 1.1 (377.3 m/s). 2.611 x 10^6 Joules, Wall level For a Mid-End, we will assume Mach 1.8 (617.4 m/s). 6.991 x 10^6 Joules, Wall level+ For a High-End, we will assume Mach 2.5 (857.5 m/s). 1.349 x 10^7 Joules, Wall level+ Tallies Detritus Makes a Back Door (Low-End): 8.552 x 10^6 Joules, Wall level+ Detritus Makes a Back Door (High-End): 2.191 x 10^7 Joules, Room level Detritus Shoots Supersonic Shrapnel (Low-End): 2.611 x 10^6 Joules, Wall level Detritus Shoots Supersonic Shrapnel (Mid-End): 6.991 x 10^6 Joules, Wall level+ Detritus Shoots Supersonic Shrapnel (High-End): 1.349 x 10^7 Joules, Wall level+ A bit below expected, but oh well, what can I do? Category:Blog posts Category:Discworld